In 1992 Unser and colleagues proved that the sequence of normalized and scaled B-splines Bm tends to the Gaussian function as the order m increases, [1]. In this article the result of Unser et al. is extended to the derivatives of the B-splines. As a consequence, a certain sequence of wavelets defined by B-splines, tends to the famous Mexican hat wavelet. Another consequence can be observed in the continuous wavelet transform (CWT) of a function analyzed with different B-spline wavelets.
B-splines; Gaussian function; Continuous wavelet transform; Mexican hat wavelet; Scalogram
